Hello everybody, recently I've been trying to unravel the secrets to breeding the perfect Pokemon.
Now this guide will eventually (hopefully) contain every single piece of information regarding breeding the perfect Pokemon. and will be even more helpful than Bulbapedia and Serebii
If anybody has any good information that is not up here please post and I'll add it as soon as possible.
So far all the information I have will be regarding Gen V and onwards simply because I don't have any DPPt games to work with.
Copyright shizz:

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You may not steal, repost or claim any part of this guide as your own.
You may quote, reference, and link this guide provided you have credited the author (Me).
I do not own nor have I had any part in the creation of Pokemon nor its respective affiliates.

Okay so..

The Basics
Contents:
How to Breed
Egg groups
Why egg groups?
What is a baby Pokemon

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Let's start a the beginning I suppose.

Now.. Within the world of Pokemon there is a place in every region where a lovely old couple will look after your Pokemon and raise them for a small fee.

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Cost($) = 100x(levels gained) + 100

You may have noticed sometimes that if you have left two Pokemon with them at any time they have an egg for you to raise. Hence the purpose of this guide.
The mechanics of breeding are here:

The game counts your steps to determine egg cycles (Or the time it takes to hatch an egg)
One egg cycle is the highest amount of steps in 2 digits the game can process. Which would be FF or 255 in normal numbers.
So one egg cycle is 255 steps
Nosepass takes 21 egg cycles to hatch so 21 x 255 = 5,355 steps.

To speed this up you can have a pokemon with Magma Armour or Flame Body as an ability to halve the amount of steps you need.

Now we know we can breed how can we breed something we want?
The most important thing to note with breeding is that the baby will ALWAYS be the same species as the MOTHER. Unless the mother is ditto in which the case the father will be the same species (We'll get back to breeding with ditto).
The easiest way to breed is to get two of the same species right? YES! (Please note that whenever I say species, I am referring to the entire evolutionary family, so if I say the Pikachu family I am referring to Pikachu, Raichu and Pichu. If I say Abra species I am referring to Abra, Kadabra and Alakazam )
But you can also breed two Pokemon of different species. The two Pokemon must be in the same Egg group.
If you're interested you can find a list of these on Bulbapedia or Pokemondb but for convenience I'l post it here. BREEDING GROUPS

It is important to note that any Pokemon that is genderless can only breed with Ditto.

Undiscovered

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This group includes all legendary Pokemon (except Phione and Manaphy) as well as the female Nidoran line and all baby Pokemon. This group will not breed no matter how long you leave them in daycare

Any of these Pokemon species can breed if you have a male and a female and they're in the same egg group.
Here's how you know if they'll breed

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Same species and different ID number
"The two seem to get along very well"
69.87% chance of getting an egg every 255 steps

Same species, same ID number
"The two seem to get along"
49.5% chance every 255 steps

Different species same ID number
"The two don't seem to like each other"
19.81% chance of an egg every 255 steps.

Different species different ID number
"The two seem to get along"
49.5% chance ever 255 steps

Different egg group, same gender, or undiscovered egg group
"The two prefer to play with other Pokemon"
0% chance to get an egg

But why would you want to breed with a different species?
The answer, to get a Pokemon with egg moves.

Egg moves are moves a Pokemon can only learn via breeding a Male with a move you want to have the baby learn with a female of the species you want.
For example, the Bulbasaur line can earn Ingrain but only via breeding.
I'll explain this in depth more in the next section.

This is easy, a lot of baby Pokemon must be bread for.
Happiny, Chingling, Azurill etc. Simply breed Pokemon of the same evolutionary family.
HOWEVER!
Some require you to breed while holding an item (Incense generally)It does not matter whether the mother or father holds the item as long as one of them have it.

The reason for this is because breeding was not possible in Gen I therefore no baby Pokemon were introduced until Gen II. When Baby Pokemon were introduced for Gen II Pokemon in Gen III (Azurill) it would be awkward to have bred a Marill in gen II and not received an Azurill simply because it didn't exist until 3rd Gen. To make sense of new baby Pokemon the game designers decided to make the parents hold an item to get the baby. And an item not in Gen II means the criterion weren't met therefore no Azurill. Logic!

Breeding For Moves

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So in my previous example Bulbasaur can possibly be bred to have Ingrain as a move. Bulbasaur is in the egg group Grass and Monster, so who is in either of these groups that can learn Ingrain?
Let's go with Roselia, this Pokemon learns ingrain at level 33.
So now I make sure to have a female of the Bulbasaur family and a male Roselia with Ingrain.
Sounds simple enough right? Right. Not much to it.
You can also breed for TM moves, and level moves and move tutor moves.

SO based on my example you should be able to breed your own favourite egg moves onto all your babies!

Breeding for Natures

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Having the right nature is imperative for competitive battling so why bother sift through what could be hundreds of eggs to find an Adamant Larvitar? A very helpful item has the ability to transfer natures from the mother to baby Pokemon.
You know, the tool you dropped in earlier games because why wouldn't you want to evolve your Pokemon?
That's right. Give the mother an Everstone to hold and you will have a 50% chance of a Modest Litwick.

If however you are breeding with a Ditto, the Ditto will be the one that holds the Everstone, despite the other Pokmon being Female.

IVs
No doubt the most frustrating part if breeding.

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It is incredibly difficult to get a Pokemon with decent IVs via breeding naturally. Of course you can turn to RNG but some don't like the idea,

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Or Windows

Breeding for this is very time consuming and you will find yourself often filling boxes of level 1 Pokemon you will have to release later on.
Now ideally we're breeding for 31 in everything. But because of the incredibly low chance of that happening naturally it is recommended to aim for Iv's above 25 in only the states you will be using.
Game Freak have made it thankfully easier to get good sets by introducing Power Items.

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Power Weight (HP)
Power Bracer (Attack)
Power Belt (Defense)
Power Lens (Sp.Atk)
Power Band (Sp.Def)
Power Anklet (Speed)

Highly useful in the sense that add 4 Effort Values (EV's) to their specified stat for every battle. They also transfer their specified stat's IV from the holder to their offspring.

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Say for example I want a Physical Sweeper Lucario and I have a ditto with 30 IV's in Attack. If Ditto is holding the Power Bracer all eggs will have 30 Iv's in Attack also.

Be careful when using two Power items however as the possibilities of having the Iv's transferred 50% for each stat.

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It IS possible to transfer both stats using two power items, I'll explain this later.

Well that's not so hard. And remember if you breed a female with the right nature but not the right stats you can switch ditto for the female with an ever stone to make it easier to get the right nature. GOOD LUCK!!

Abilities

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This section is so small.
If the Pokemon you wish to breed has dual abilities, there is a 50% of getting either.
If you are breeding with a Pokemon that has it's Dream World ability their is a 50% chance of getting the Dream World ability and 25% chance of the other two.

Gender

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This Section is even smaller
The possibility of breeding either gender depends on the Species.
The most common is 50-50 such as Nosepass
But you may have found already it is especially difficult to breed a female Eevee this is because Eevee has only 12.5% chance of getting a female
This works exactly the same as in the wild.

The purpose of this is to breed moves across egg groups.
The Catalyst Pokemon (Pikachu and Nidoran in these examples) always has two egg groups otherwise rendering them redundant. On most occasions from the Pokemon with the moves group to the target Pokemon's group.

It is possible to chain across multiple egg groups with multiple chains. Just make sure you are breeding for males (derp). Never teach a female a move tutor move. Just in case you need to breed the move and can't get that move taught again.
You can always breed the male with the move for another female.

And that is basically It.

Chaining for IVs

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IVs are not all generated random as you may already know. In fact without using power items your Pokemon will inherit 2 to 5 of it's parents IV's.
The rest are generated randomly.
It is generated with priority like this:

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1) Power items
2) One random stat from either parent (Not HP or Def)
3) One random stat from either parent (Not HP)
4) Two random stats from opposite parents

Of course that's IF they inherit the stats, sometimes you will find that no stats will be inherited that I believe is because (don't be flaming if I'm wrong here) is because the stat chosen for the random stats inherited was HP and or HP or Def which is removed by the game.

So because of this, each two that are the same stat are overwritten by the higher priority.

So you would think to put two Power items on to increase the likelihood of getting two good stats. Well not necessarily true. You have 50% chance of either occurring but the likelihood of the other will be randomly assigned as normal.

The trick to chain IV breeding, is that when you find a baby with more IVs in all the stats you switch one of the Pokemon out, and give it a new power item (or Everstone).
Not all that difficult once you have the hang of it.

Some people find that breeding for correct IVs and Natures far too tedious if that person is you open this spoiler.

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So you're too lazy to put more effort into breeding..
Well okay then, I bet you want to know what is more effective when you get to level 100 having 31 IVs or having a beneficial nature right?

BASE STAT < 121, you will benefit more with 31 IVs and neutral nature
BASE STAT > 126, you will benefit more from a beneficial nature and 0 IVs
*With 252 EVs

Of course both is ideal don't get confused.

I soon hope to add more information on each section as well as my experience trying to breed an almost perfect IV spread from a Scyther with IVs (16, 4, 1, 8, 15, 8) without catching another.
Which I have started on my quest you can see my progress in this spoiler where I'll explain everything I have done.

Darwin's Theory within Pokemon Experiment:

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Here we go..
First I should explain that I have two Ditto's I will be using throughout the course of this experiment.
DITTO 30, 30, 3, 24, 28, 8 Sassy
and Ditto 20, 9, 16, 31, 11, 31

Who doesn't love cramming as many spoilers into a post as they can?
Okay so first session began at 8:03am and finished 11:33am
I started with a possible two 30 or higher stats in HP and Atk on the ditto, to which I switched Scythers and Ditto's to make a possible three.
I think sacrificed perfect SpA for higher SpD
Then switched for higher Defence
I then got lucky in which the daughter Scyther inherited both HP and Atk from Naughty Scyther as well as Rash Scythers Speed, she also has an Adamant nature which is what I was looking for.
We'll see how dual 30+ IV's turn out

No one hesitate to add information or ask questions, like it says in the title this is on-going I'll be adding whenever I find new info.